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Posted by Moby Dick
on 7/8/2009, 9:08 am, in reply to "A Major Challenge for True Puzzlers"
Before doing any work on this, I would like to ensure that my understanding of the requirement is correct. Here's my understanding of it:
* there are 14 teams entering a competition
* you wish to produce a unique ordering in the fewest number of games that would be accurate if each team had played to the best of its ability in each game
If so, then my suggestion would be to abandon the idea of fixing any of the fixtures (except the first) in advance, and instead decide the fixtures after each round using a Swiss Tournament system (click here).
If you still want us to work on optimising a fixed selection for the first 4 games for 14 teams, then please clarify how the play-off will work. Is it that all teams that have the same number of points will play each other in a mini-league?
Or is it that you just want us to come up with a method of making a fixture permutation for 14 teams playing 4 games each that ensures that each combination of 2 teams has either played each other or have at least one opponent in common?
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